Let g(x)= -2(3x+4)(x−1)(x−3)^2 be a polynomial function. Name all horizontal and vertical intercepts of the graph. State the end behavior of g.

The vertical intercepts is

(4/3,0) (3,0) (1,0)

The horinzontial intercepts is

(0,72)

The end behavior is

as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Step-by-step explanation:

The vertical or y intercepts will be zeroes of the following factors.

We solve for x each time.

Part B). We need to find the intercepts by setting the equation equal to zero.

The constant expanded will equal 72.

If x=0,

where y is any real number.

So this means all the exponets will equal 0. The constant will just add to the term. so our horinzontal intercept is

Part C) End Behavior

The leading degree is even. Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.

Our leading coefficient is negative so this means our quadratic will get reflected across the x axis.

Now this means, as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."